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AWARDS AND HONORS
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CHIMIA 2002, 56, No. 1/2
Chimia 56 (2002) 13–19
© Schweizerische Chemische Gesellschaft
ISSN 0009–4293
Hybrid QM/MM Car-Parrinello
Simulations of Catalytic and
Enzymatic Reactions
Maria Carola Colombo, Leonardo Guidoni, Alessandro Laio, Alessandra Magistrato, Patrick
Maurer, Stefano Piana, Ute Röhrig, Katrin Spiegel, Marialore Sulpizi, Joost VandeVondele,
Martin Zumstein, and Ursula Röthlisberger*a
aRuzicka
Prize Winner 2000
Abstract: First-principles molecular dynamics (Car-Parrinello) simulations based on density functional theory
have emerged as a powerful tool for the study of physical, chemical and biological systems. At present, using
parallel computers, systems of a few hundreds of atoms can be routinely investigated. By extending this
method to a mixed quantum mechanical – molecular mechanical (QM/MM) hybrid scheme, the system size can
be enlarged further. Such an approach is especially attractive for the in situ investigation of chemical reactions
that occur in a complex and heterogeneous environment. Here, we review some recent applications of hybrid
Car-Parrinello simulations of chemical and biological systems as illustrative examples of the current potential
and limitations of this promising novel technique.
Keywords: Car-Parrinello first-principles molecular dynamics · Computational chemistry ·
Enantioselective catalysis · Enzymatic reactions · QM/MM simulations
Ursula Röthlisberger was born in Solothurn. In
1988 she made her diploma in physical chemistry in the group of Prof. Ernst Schumacher at
the University of Bern. Her Ph.D. thesis was
undertaken in collaboration with Dr. Wanda
Andreoni at the IBM Zurich Research Laboratory in Rüschlikon. After completing her PhD
in 1991 she spent some time as a postdoctoral research assistant at the IBM Research
Lab. From 1992–1995 she was a postdoctoral
research assistant in the group of Prof.
Michael L. Klein at the University of Pennsylvania in Philadelphia (USA). In 1994 she was
awarded an advanced researcher fellowship
(Profile 2) from the Swiss National Science
Foundation. Before taking up her Profile 2 fellowship she spent another year as postdoctoral research assistant in the group of Prof.
Michele Parrinello at the Max-Planck Institute
for Solid State Physics in Stuttgart, Germany.
In 1996 she moved as Profile 2-fellow to the
ETH in Zurich, hosted by the group of Prof.
Wilfred F. van Gunsteren. In 1997 she became
Assistant Professor of Computer-Aided Inorganic Chemistry at the ETH Zurich.
*Correspondence: Prof. Dr. U. Röthlisberger
Tel.: +41 1 632 7460
Fax: +41 1 632 1090
E-Mail: [email protected]
Laboratorium für Anorganische Chemie
ETH Hönggerberg
Wolfgang Pauli Str. 10
CH–8093 Zürich
1. Introduction
During the last decade the field of computational chemistry has experienced
enormous progress. Due to the exponential increase in computer power and
the development of new computational
methods it has now become possible to
treat many complex chemical and biological problems on an accurate and realistic
level.
First-principles molecular dynamics
(MD) simulations [1] based on density
functional theory (DFT) [2] and mixed
quantum mechanical/molecular mechanical (QM/MM) approaches [3] are among
the most powerful of these new computational tools. We have recently developed
a combination of these two techniques
into a hybrid QM/MM Car-Parrinello
scheme [4]. This approach enables efficient and robust hybrid Car-Parrinello
simulations of extended systems in
which the chemically relevant part is
treated at the quantum mechanical level
while the effects of the surroundings are
taken explicitly into account through the
embedding in a classical environment.
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CHIMIA 2002, 56, No. 1/2
Hybrid QM/MM Car-Parrinello simulations paired with enhanced sampling
techniques [5] are especially attractive
for the in situ investigation of complex
chemical and biochemical reactions that
occur in a heterogeneous environment.
In this article, we shortly summarize
some of the pertinent features of our
hybrid implementation and review some
recent applications of this technique to
chemical and biochemical systems as
representative examples of the type of
problems that can be tackled with this
method.
H = HQM + HMM + HQM
/MM
(1)
(2)
(3)
(4)
(5)
2. Computational Method
The computer simulation of chemical
reactions in realistic environments is a
particularly challenging task. The fact
that chemical bonds are broken and
formed during this process necessitates
the use of a quantum mechanical method
which can take explicit account of the
instantaneous changes in the electronic
structure. Furthermore, electronic correlation effects are known to be important
for an accurate description of reaction
barriers and consequently, only relatively
elaborate electronic structure approaches
can be applied. However, traditionally
correlated quantum chemical methods
are restricted to the treatment of relatively small systems in the gas phase whereas
complex chemical and biochemical processes usually occur in heterogeneous
condensed phase environments consisting of thousands of atoms.
One possible solution for the modelling of such systems is the choice of a
hierarchical hybrid approach in which the
whole system is partitioned into a localized chemically active region (treated
with a quantum mechanical method) and
its environment (treated with empirical
potentials). This is the so-called quantum
mechanical/molecular mechanics (QM/
MM) method, in which the computational effort can be concentrated on the part
of the system where it is most needed
whereas the effects of the surroundings
are taken into account with a more expedient model.
The particular QM/MM Car-Parrinello method [4] that has been used in this
paper is based on a mixed Hamiltonian of
the form (Eqn. (1)) in which the quantum
part HQM is described with the extended
Car-Parrinello Lagrangian (Eqn. (2))
where MI and are the nuclear mass and
position,
are one-particle wavefunctions, µ is the mass associated with the
fictitious classical kinetic energy of the
(6)
(7)
electronic degrees of freedom, and the
Lagrange parameters Λi,j enforce orthogonality of the electronic wave functions.
The potential energy term
is
given by the Kohn-Sham energy density
functional (Eqn. (3)) where
is the
external potential,
the exchangecorrelation functional and the electron
density
is given by Eqn. (4).
In our hybrid QM/MM simulations,
we use a standard Car-Parrinello implementation [6], in which the one-electron
wave functions are expanded in a basis
set of plane waves and only the valence
electrons are treated explicitly whereas
the ionic cores are integrated out using
norm-conserving non-local pseudo potentials [7].
The purely classical part of the Hamiltonian in Eqn. (1), HMM, is described
by a standard biomolecular force field
(Eqn. (5)) where
and
are of the general form (Eqn. (6) and
(Eqn. (7)).
The terms in
take harmonic
bond, angle and dihedral terms and the
ones in
electrostatic point
charge and van der Waals interactions
into account.
The intricacies of QM/MM methods
lie in the challenge of finding an appropriate treatment for the coupling between
QM and MM regions as described by the
interaction Hamiltonian HQM/MM. Special
care has to be taken that the QM/MM interface is described in an accurate and
consistent way, in particular in combination with a plane wave based Car-Parrinello scheme. Several mixed QM/MM
Car-Parrinello methods have recently
been implemented [8][9]. In the fully
Hamiltonian coupling scheme developed
in our group [4], bonds between QM and
MM part of the system are treated with
specifically designed monovalent pseudo
potentials whereas the remaining bonding interactions of the interface region,
i.e. angle bending and dihedral distortions, are described on the level of the
classical force field. The same holds for
the van der Waals interactions between
QM and MM parts of the system. The
electrostatic effects of the classical environment on the other hand, are taken into
account in the quantum mechanical description as additional contribution to the
external field of the quantum system
(8)
where qi is the classical point charge located at ri and vi(|r – ri|) is a Coulombic
interaction potential modified at shortrange in such a way as to avoid spill-out
of the electron density to nearby positively charged classical point charges. In the
context of a plane wave based Car-Parrinello scheme, a direct evaluation of
Eqn. (8) is prohibitive as it involves of
the order of NrxNMM operations, where
Nr is the number of real space grid points
(typically ca. 1003) and NMM is the
number of classical atoms (usually of the
order of 10,000 or more in systems of biochemical relevance). Therefore, the interaction between the QM system and the
more distant MM atoms is included via
a Hamiltonian term explicitly coupling
the multipole moments of the quantum
charge distribution with the classical
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CHIMIA 2002, 56, No. 1/2
point charges. This QM/MM Car-Parrinello implementation [4] establishes an
interface between the Car-Parrinello
code CPMD [10] and the classical force
fields GROMOS96 [11] and AMBER95
[12] in combination with a particle-particle-particle mesh (P3M) treatment of the
long-range electrostatic interactions [13].
In this way, efficient and consistent
QM/MM Car-Parrinello simulations of
complex extended systems of several
10’000–100’000 atoms can be performed
in which the steric and electrostatic effects of the environment are taken explicitly into account.
This complex is a catalyst precursor
for the highly enantioselective hydrosilylation of norbornene, styrene and other
olefins with HSiCl3 [17]. As shown in the
Table, it presents such remarkable structural features as a ‘world-record’ Pd–P
bond length of as much 2.50 Å and a
rather pronounced deviation from ideal
square planar geometry as indicated by
the angle between the P-Pd-N and Si-PdSi planes of 34°.
By constructing a systematic series of
different QM and QM/MM models (also
shown in Fig. 1) the nature of the Pd–P
bond elongation and the origin of the
non-square-planar coordination geometry of the Pd center can be traced back to
the different molecular components.
Steric versus electronic effects can be
separated clearly by allowing only for
steric contributions of the MM fragments
while the electrostatic coupling is explicitly suppressed. A comparison of the
structural features of the different computational models (Table) demonstrates
that much of the extreme lengthening of
the Pd–P bond is due to the steric interaction between the phenyl groups of the
3. Applications
In the following sections, we present
a few selected examples of hybrid QM/
MM Car-Parrinello applications in order
to illustrate the type of problems that can
be treated with this method.
3.1. Organometallic Transition
Metal Complexes and
Enantioselective Catalysis
Due to the importance of correlation
effects, an accurate description of transition metals is a highly demanding task for
quantum mechanical electronic structure
approaches. Density functional methods
[2] have a long tradition in the treatment
of such systems and constitute an attractive compromise between accuracy and
computational cost. Nowadays, organometallic transition metal complexes of
the size of a few hundreds of atoms can
be treated entirely at the quantum mechanical level [14]. Nevertheless, QM/MM
methods are a handy tool also for these
systems as they allow for an easy dissection of electronic and steric effects of different parts of the molecule. An example
for the use of combined QM/MM calculations as such an analytic tool has recently been performed [15] for the chiral
bis(trichlorosilyl)-palladium(II) complex
shown in Fig. 1.
Table. Comparison of selected geometric parameters derived from the experimental X-ray
structure and those of various computational
models (see Fig. 1). In the QM/MM models only
steric contributions of the MM fragment are
allowed to contribute [15]. Distances are reported in Å and angles in deg. Si(1): silicon
atom in trans position to P; Si(2): silicon atom in
trans position to N.
Fig. 1. Different computational models of a chiral palladium(II)-bis(trichlorosilyl) complex. A: full
quantum model (DFT with BP86 gradient corrections [16]); B: minimal quantum model; C: QM/
MM model 1 and D: QM/MM model 2. The parts that are shown in light blue lines constitute the
MM part. Only steric contributions of the MM fragment are allowed to contribute [15].
parameter
X-ray
Full QM
Small QM
QM/MM-1
QM/MM-2
Pd-P
2.50
2.53
2.39
2.46
2.50
Pd-N
2.21
2.25
2.18
2.20
2.21
Pd-Si(1)
2.31
2.33
2.33
2.32
2.32
Pd-Si(2)
2.26
2.29
2.29
2.28
2.28
N-Pd-Si
154
159
167
158
154
P-Pd-Si
157
154
165
159
157
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CHIMIA 2002, 56, No. 1/2
phosphine and the trimethylphenyl group
of the pyrazole ring [15].
Similar QM/MM calculations as the
one described have also proven to be useful in evaluating the structural effects of
π–π stacking interactions in organometallic complexes [18]. Besides serving as
an analytic tool, QM/MM models provide also computationally highly efficient, realistic models that make the detailed investigation of entire catalytic reactions cycles, in which many different
adduct structures and reactive pathways
have to be considered, feasible. Detailed
QM/MM Car-Parrinello simulations of
the enantioselective palladium catalyzed
hydrosilylation of styrene [19] and the
mechanism of catalytic enantioselective
fluorination [20] in gas phase and acetonitrile solution are recent example of
this type of applications.
3.2. Design of Biomimetic
Compounds
During millions of years of evolution,
nature has developed its own mild and
efficient way of doing chemistry. Enzymes, the cell’s chemical laboratories,
are able to catalyze a large variety of biologically relevant chemical reactions
with high efficiency and selectivity. In
many cases, laboratory experiments have
to resort to extreme pressures and temperatures to perform reactions that are
easily carried out in living cells at ambient conditions. The idea of synthesizing enzyme mimics therefore emerges
quite naturally. Many research groups
throughout the world are working on reaction schemes that adopt biochemical
strategies with the goal of finding ‘green
chemistry’ routes with higher efficiency
and/or selectivity. One especially attractive strategy is to map the essential catalytic properties of the natural system on
to relatively simple synthetic compounds
that can easily be handled and modified
for specific purposes. However, due to
the large complexity of biological systems, the development of functionally
equivalent biomimetic compounds has
met with great difficulties.
In this field, computer simulations, in
which the role of different active site residues can be probed systematically, can
make important contributions in trying to
pinpoint the essential catalytic features
of an enzymatic process, as well as in
the subsequent design of simplified biomimetic analogues.
We have recently performed a parallel study of the copper enzyme galactose
oxidase (GOase) and existing low-efficiency mimics [21] (Fig. 2). GOase oxi-
dizes primary alcohols selectively to the
corresponding aldehydes and is therefore
of interest as a potential (stereo)selective,
mild oxidation catalyst. This is of special
importance in view of the fact that even
though selective oxidation is of key importance for many industrial applications
(e.g. in the preparation of perfumes and
UV-stabilizers), to date relatively expensive and hazardous chemicals (such as
e.g. RuO4– or KMnO4) are used for this
purpose [23].
By applying mixed QM/MM CarParrinello simulations, the natural and a
low-efficient synthetic system (shown in
Fig. 2) were confronted step by step
throughout the catalytic cycle, and mutual differences were identified [21]. This
comparative study showed that the overall features of the mimetic compound are
qualitatively remarkably similar to the
ones of its natural target. However, important differences exist in the activation
energy of the rate-determining step of the
reaction, which involves the abstraction
of a hydrogen atom in an antiferromagnetically coupled diradical species. The
overall geometric features of the corresponding transition states are very similar. However, a detailed characterization
of their electronic structure provides a
possible rationale for the decreased efficiency of the synthetic system. In fact,
our calculations show that in the natural
system, the unpaired electron density of
the intermediate ketyl radical is in part
delocalized over an equatorial ligand of
the copper coordination sphere. Due to an
unfavorable geometric orientation, the
analogous effect is not present in the synthetic compound resulting in a difference
in the corresponding activation energies
of 5 kcal/mol.
This is a clear example of the fact that
a subtle electronic effect can play a decisive role in determining the catalytic
properties of a system. This electronic influence can only be detected with an electronic structure calculation and cannot
be captured by a design strategy that is
merely based on geometric parameters.
The crucial (electronic) factors that determine the height of the activation barrier
in the rate-determining catalytic step that
Fig. 2. The copper enzyme galactose oxidase (GOase) (A) and its active site (B) in comparison with
a functional biomimetic compound (C) [22].
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CHIMIA 2002, 56, No. 1/2
have been identified in this study were
subsequently used to design a new generation of synthetic compounds. QM/MM
Car-Parrinello calculations performed on
these newly designed models predict an
improvement of several orders of magnitude in the catalytic efficiency, making it
similar to (or higher than) that of the natural system.
3.3. Locating Copper-Binding Sites
in Prion Proteins
Prions are infectious agents that play
a central role for a group of invariably fatal, neurodegenerative diseases affecting
animals such as sheep (scrapie), cattle
(BSE), and humans (e.g. variants of the
Creutzfeldt-Jacob disease) [24]. It is now
widely established that these diseases are
caused by an abnormal isoform PrPSc of
the normal cellular prion protein PrPC
[25]. Recent experiments, both in vivo
and in vitro, indicate that prions are able
to bind metal ions, in particular Cu2+
[26]. It has generally been assumed that
Cu2+ ions bind to the histidine-rich unstructured part [27]. However, recent pulse
EPR and ENDOR experiments [28] suggest that copper binds with higher affinity
in the structured part (amino acids residues 125–228). Three pH-dependent copper
binding sites have been identified together
with some information about the nature
of the immediate copper coordination
sphere. The exact position of the metal
binding sites within the protein, however,
could not be localized experimentally.
An identification of the copper binding sites in the structured part of prion
proteins and a detailed characterization
of the metal protein interactions are of
great interest, as it has been suggested
that metal ions could influence the structural stability and, potentially, also the
transition to the infectious scrapie form.
Moreover, the interplay with metal ions
is a common denominator for several
other neurodegenerative disorders such
as Alzheimer’s, Parkinson’s and amylotrophic sclerosis [25].
Starting from the available NMR
structure of the metal-free mouse PrPC
[30], we have performed mixed QM/MM
Car-Parrinello simulations with the aim
of identifying likely locations for Cu2+
binding [31].
Locating (transition) metal ions in a
protein structure is a particularly cumbersome task, since the intricate nature of
the bonding properties of the metal necessitates the use of a quantum mechanical electronic structure approach. At the
same time the protein environment and
solvent have to be taken into account,
as well as dynamical finite temperature
effects. A QM/MM approach appears
therefore as the method of choice. However, since it is a priori not known which
ligands are involved in binding, the necessary partitioning of the system into QM
and MM regions is far from trivial. To
circumvent this problem, we first performed a statistical analysis of all available high resolution (≤2 Å) crystal structures of copper proteins, to determine the
relative propensity of different amino acids for copper ligation. Using this probability map, we scanned the structure of
the mouse prion protein for the most likely Cu2+ binding regions. The resulting
candidate structures were ranked by increasing probability and their stability
was subsequently tested in QM/MM CarParrinello simulations of several picoseconds around room temperature. The starting point of all simulations was the experimentally determined NMR structure,
which was immersed in a box of water
and equilibrated by classical molecular
dynamics simulations. Subsequently, a
Cu2+ ion was placed in the vicinity of selected residues included in the QM region, and the exact location of the Cu2+
Fig. 3. Potential copper binding site in the
structured part of the murine prion protein.
Atoms that constitute the quantum part are
indicated in thick cylinders, the classical environment with thin sticks. A contour plot of the
unpaired spin density is shown in cyan.
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CHIMIA 2002, 56, No. 1/2
glet state. This combination allows the
investigation of photochemical processes
in complex biological systems. As a first
test case study, we are currently investigating the cis-trans photo-isomerization
in rhodopsin. Our model system (24000
atoms, see Fig. 4) contains the protein, a
hydrophobic membrane-mimetic environment consisting of octane, and a saline solution. This setup is based on the
most recent crystal structure of rhodopsin
and results in a stable classical MD of
several nanoseconds without imposing
any type of structural constraint [35].
The key configurations of these classical pre-equilibration runs are currently
used for mixed QM/MM simulations of
ion and its coordination were determined
in mixed QM/MM Car-Parrinello simulations. We have performed calculations
on several binding sites, one of which is
shown in Fig. 3. This possible binding
site is approximately axial square planar
and involves Met138, His140, and
Asp147 as equatorial and a water molecule as axial ligand. The detailed coordination spheres that have been determined
in the simulations can now be tested via
site-directed mutagenesis experiments.
3.4. Investigation of the First Step
of Human Vision
Human vision is a highly efficient
process in which light is transformed into
a neuronal signal that is detected in the
brain. In the first step of this biochemical
reaction chain, the transmembrane protein rhodopsin, which is located in the
retina, plays the predominant role [32].
Rhodopsin consists of seven transmembrane helices accommodating in their
middle the covalently bound chromophore, the protonated Schiff base of
11-cis retinal. Upon exposure to light,
retinal isomerizes from 11-cis to all-trans
in an extremely fast and efficient process,
which is completed within 200 fs with a
quantum yield of 0.67 (Scheme 1).
This induces a structural change of
the intracellular part of the protein and
triggers the signal transduction to another
receptor protein of the signal cascade. A
mechanistic understanding of this primary reaction is not only essential with regard to the cure of some eye diseases, but
also of great interest for the development
of optical switches.
The recent X-ray structure of rhodopsin [33] has paved the way to a
molecular investigation of the activation
mechanism. However, a detailed mechanistic understanding is still lacking. The
role of the protein environment that promotes the isomerization reaction is not
well understood. Also, the conformational changes that accompany the accommodation of all-trans retinal within the tight
binding pocket are unknown. From a theoretical point of view, the investigation
of these questions requires a mixed quantum/classical approach, because the excited state dynamics of retinal (50 atoms)
is a quantum chemical process, while the
description of the whole protein (about
5600 atoms) is only feasible within a
classical framework.
We have recently combined our
mixed QM/MM Car-Parrinello approach
[4] with the restricted-open shell KohnSham (ROKS) [34] method for describing the dynamics in the first excited sin-
Scheme 1
Fig. 4. Simulation system for rhodopsin. The protein (blue) contains seven transmembrane
helices which accommodate the chromophore (yellow) in the middle. The membrane is mimicked
by an octane solution (turquoise) surrounded by water (red sticks). Internal water molecules are
indicated as red balls.
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the initial reactant state and the ROKSQM/MM Car-Parrinello simulations of
the isomerization in the excited state.
Acknowledgements
U. Röthlisberger thanks the Swiss National
Science Foundation (Grant Nos. 21–57250.99
and 21–63766.00), the ETH Zurich and the
Roche foundation for financial support.
J. VandeVondele, U. Röhrig and M. Colombo
acknowledge ICARUS, MINOS and CNR fellowships.
Received: January 16, 2002
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